Miniature cable harness assemblies are commonly used to connect to input/output ports at the rear of IC (integrated circuit) Cards. A common design for a harness assembly includes a connector frame holding multiple contacts, a circuit board extending rearward of the connector frame, and a stripped cable held to the rear of the board. A row of conductive traces lie at the front of the board, and insulated wires of the cable extend to the traces. The bared front end of each wire is soldered to a trace, and tail of each contact is also soldered to a trace, to form a joint that connects them. After the joints are made, the assembly is placed in mold and insulative plastic is molded around the joints and wires to form a first molded layer. Then a layer of copper foil is wrapped round the first layer and the braided shielding of the cable is soldered to the foil. Finally, the assembly is placed in an overmold in which insulative plastic is injected to surround the foil and shielding and to form the outline of the harness assembly. The need to apply three layer over the initial assembly of board, wires, contact tails, and joints, with two of the layers being injection molded and one of them being a foil wrap, add to the cost and bulk of the assembly. Each of the two injection molding steps adds to the cost due to the dies and injection molding time, while the handling of foil wrapping adds additional costs. A compact cable harness assembly which could be constructed at low cost would be of value.